7.4 introduction to robot kinematics | manipulator kinematics | two wheel differential chassis kinematics | wheel odometer

The author of this series of tutorials ： Little fish
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7.4 Introduction to robot kinematics

Robotics is a very huge subject , Anything related to robot design and application can be divided into Robotics , Mainly kinematics and dynamics 、 System structure 、 Sensing technology 、 Motion planning technology 、 Decision making technology, etc .

In order to facilitate the later robot modeling and simulation , In this section, we briefly introduce and learn the kinematics of the robot .

1. Robot kinematics

Robot kinematics studies the pose relationship of robots , It mainly includes forward kinematics and inverse kinematics .

Forward kinematics is to give the variables of each joint of the robot , Calculate the position and attitude of the end of the robot ; For example, last class we knew the relationship between robot joints and joints , Seeking joint 1 And joints 3 The relationship between

Inverse kinematics is to know the position and attitude of the end of the robot , Reverse the joint variables of the robot ; For example, when we know robot joints 1 And joints 3 The relationship between , Find the joint 1 And joints 2, The joints 2 And joints 3 The relationship between .

2. Introduction to manipulator kinematics

Forward kinematics ： The angle of each joint is known , Find the pose of the end

Inverse kinematics ： Known end attitude , Find the angle of each joint

3. Introduction to kinematics of two wheel differential chassis

The two wheel differential model refers to the chassis model of the robot chassis, which is composed of two driving wheels and several supporting wheels , image turtlebot And open source robots fishbot Both are two wheel differential models .

The two wheel differential model can pass through different speeds and steering through two driving wheels , Make the robot reach a specific angular velocity and linear velocity .

You've all seen the two wheeled balance car , You can move back and forth by relying on two wheels （ Linear velocity ）, Turn left and turn right （ angular velocity ）.

3.1 Positive and inverse solution

Understand the two wheel differential model , What about the forward and inverse solutions ？

Forward kinematics ： Given the speed of the two wheels , Find the angular velocity of the whole vehicle （ radian / second ） And linear velocity （ rice / second ）

Inverse kinematics ： The angular velocity and linear velocity of the target are known , Find the speed of the two wheels

3.2 Wheel odometer

When we know the relative position between the two wheels , At the same time, we know the angular velocity and linear velocity of the robot at each moment , So how do we get the current angle and position of the robot ？

3.2.1 angle

There is only one factor that affects the current angle of the robot , It's angular velocity .

The rotation angle of the robot at a certain time = The angular velocity of the robot at this moment * This moment is long

If we determine that the angle of the robot at the initial time is 0, By accumulating the rotation angle of the robot , You can get the current angle of the robot .

In fact, the above process is to integrate the diagonal velocity to get the angle .

3.2.2 Location

Through the diagonal velocity integral , We got the angle .

The forward speed of the robot in its own direction at a certain time can be decomposed into the odometer coordinate system x Axis and y Speed in the axial direction .

As you can see from the diagram ：
$$\begin{gathered} v_y=v\ast cos(\theta ) \\ {v}_y=v\ast sin(\theta ) \end{gathered}$$
Got it x and y Speed in direction , Multiply by the time elapsed at a certain time corresponding to this speed , You can get this moment in x Axis and y Displacement in the direction of the axis , By accumulating the displacement, the... In the odometer can be obtained x and y.

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The authors introduce ：

I'm little fish , Senior players in Robotics , Now a one legged robot Algorithm Engineer in Shenzhen
Junior high school learning programming , High school began to contact robots , During the University, playing robot related competitions to achieve monthly income 2W+（ The prize money for the competition ）
Currently outputting Robot Learning Guide 、 Notes to the paper 、 Work experience , Welcome to pay attention to little fish , Exchange technology together , Learning robots